Question

A life jacket (personal flotation device) worn by commercial fishermen is designed to provide a minimum upward force on the user of 34 lbf. The foam material used in this jacket has a density of 3.2 lbm/ft3. If the remaining material (cloth, straps, fasteners, etc.) weighs 4.0 lbf and is of negligible volume, determine the minimum volume of the foam needed (ft3) for this life jacket.

Answer 1

This problem is from the fluid statics and we know that the water exerts a upward force on any object when it is partially or fully emerged in the liquid, this force is equal to the water displaced. Upward thrust required = 34 lbf Density of the foam = 3.2 lb/ft13 Let the volume of the foam used = X ftA3 Following forces are acting on the floating device. F1 F3 F2 Here F1 is acting due to the weight of the water displaced. F2 is working due to the weight of the foam and f3 is due to the weight of the cloths etc. Since the volume of the cloths are negligible. Volume of the water that will be displaced will be X ft ^3. F1 = mg Here m is the mass of water displaced. Mass m = Volume * density

Density of water is 62.4 lb ft^3. Thus m=X*624 lb F1 = 62.4x lbf F3=4 lbf F2 = 3.2*x Ibf In the limiting case when we need minimum foam we need to have a net resulting force of 34 lbf in the upward direction. Thus F1-F2-F3 = 34 lbf w 62.4X-3.2X-4 lbf = 34 Ibf I w 59.2X = 38 lbf w X = 38/59.2 =0.641 ft 3 Thus the required minimum volume of the foam is 0.641 ft^3. Hope this helps Feel free to comment in the case of any doubt. Thanks